The probability that a random multigraph is simple. II
نویسنده
چکیده
Consider a random multigraph G∗ with given vertex degrees d1, . . . , dn, constructed by the configuration model. We give a new proof of the fact that, asymptotically for a sequence of such multigraphs with the number of edges 1 2 ∑ i di → ∞, the probability that the multigraph is simple stays away from 0 if and only if ∑ i d 2 i = O (∑ i di ) . The new proof uses the method of moments, which makes it possible to use it in some applications concerning convergence in distribution. Corresponding results for bipartite graphs are included.
منابع مشابه
The Probability That a Random Multigraph is Simple
If n ≥ 1 and (di)1 is a sequence of non-negative integers, we let G(n, (di)1 ) be the random (simple) graph with the n vertices 1, . . . , n, and with vertex degrees d1, . . . , dn, uniformly chosen among all such graphs (provided that there are any such graphs at all; in particular, ∑ i di has to be even). A standard method to study G(n, (di)1 ) is to consider the related random multigraph G ∗...
متن کاملThe splitting design that leads to simple random sampling
Implementing unequal probability sampling, without replacement, is very complex and several methods have been suggested for its performance, including : Midseno design and systematic design. One of the methods that have been introduced by Devil and Tille (1998) is the splitting design that leads to simple random sampling .in this paper by completely explaining the design, with an example, we ha...
متن کاملOn Generalized Random Railways
We consider a random generalized railway defined as a random 3-regular multigraph where some vertices are regarded as switches not allowing traffic between any pair of attached edges. It is shown that the probability that the generalized railway is functioning is linear in the proportion of switches. Thus there is no threshold phenomenon for this property.
متن کاملProbability Generating Functions for Sattolo’s Algorithm
In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. Recently, H. Prodinger analysed two important random variables associated with the algorithm, and found their mean and variance. H. Mahmoud extended Prodinger’s analysis by finding limit laws for the same two random variables.The present article, starting from the ...
متن کاملDiameter and Stationary Distribution of Random $r$-out Digraphs
Let D(n, r) be a random r-out regular directed multigraph on the set of vertices {1, . . . , n}. In this work, we establish that for every r ≥ 2, there exists ηr > 0 such that diam(D(n, r)) = (1 + ηr + o(1)) logr n. Our techniques also allow us to bound some extremal quantities related to the stationary distribution of a simple random walk on D(n, r). In particular, we determine the asymptotic ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Applied Probability
دوره 51 شماره
صفحات -
تاریخ انتشار 2014